What are the divisors of 3880?

1, 2, 4, 5, 8, 10, 20, 40, 97, 194, 388, 485, 776, 970, 1940, 3880

There is a total of 16 positive divisors.
The sum of these divisors is 8820.
The arithmetic mean is 551.25.

12 even divisors

2, 4, 8, 10, 20, 40, 194, 388, 776, 970, 1940, 3880

4 odd divisors

1, 5, 97, 485

How to compute the divisors of 3880?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 3880 by each of the numbers from 1 to 3880 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

3880 / 1 = 3880 (the remainder is 0, so 1 is a divisor of 3880)
3880 / 2 = 1940 (the remainder is 0, so 2 is a divisor of 3880)
3880 / 3 = 1293.3333333333 (the remainder is 1, so 3 is not a divisor of 3880)
...
3880 / 3879 = 1.0002577984016 (the remainder is 1, so 3879 is not a divisor of 3880)
3880 / 3880 = 1 (the remainder is 0, so 3880 is a divisor of 3880)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 3880 (i.e. 62.28964600959). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

3880 / 1 = 3880 (the remainder is 0, so 1 and 3880 are divisors of 3880)
3880 / 2 = 1940 (the remainder is 0, so 2 and 1940 are divisors of 3880)
3880 / 3 = 1293.3333333333 (the remainder is 1, so 3 is not a divisor of 3880)
...
3880 / 61 = 63.606557377049 (the remainder is 37, so 61 is not a divisor of 3880)
3880 / 62 = 62.58064516129 (the remainder is 36, so 62 is not a divisor of 3880)